Alessandro Nesta netted in the first half and Ronaldinho twice after the break to push Leonardo's side eight points behind leaders Inter Milan, who beat Siena 4-3 on Saturday.
Second-placed Milan, who have a game in hand and meet Inter on Jan. 24, condemned Juve to their fourth defeat in five matches in all competitions and reports linking the Turin club with Russia coach Guus Hiddink have already re-emerged.
The visitors were far from spectacular on a cold night but third-placed Juve's confidence is so low that an average display was enough to win handsomely.
Milan doubled their lead on 72 minutes when Ronaldinho's header from a corner was deflected in by Paolo De Ceglie and the Brazilian added the third from David Beckham's cross late on.
"Inter won yesterday so we had to win this game to stay in the race," Milan's Pirlo, back to his best after the whole team struggled in Leonardo's first months in charge, told Sky TV.
"We've changed tactics and mentality. The title race is still long."
Cesare Prandelli's side have a game in hand and lie three points behind Napoli while fifth-placed AS Roma are two above the Florence club following Saturday's 1-0 win over Chievo.
Palermo are level with Fiorentina after Edinson Cavani's second-half penalty secured a 1-0 home win over strugglers Atalanta, who are poised to appoint Lino Mutti as Antonio Conte's successor as coach according to media reports.
